Rydberg blockade effects at $n\sim 300$ in strontium

Rydberg blockade at $n\sim 300$, is examined using strontium $n{}^{1}F_3$ Rydberg atoms excited in an atomic beam in a small volume defined by two tightly focused crossed laser beams. The observation of blockade for such states is challenging due to their extreme sensitivity to stray fields and the many magnetic sublevels associated with $F$ states which results in a high local density of states. Nonetheless, with a careful choice of laser polarization to selectively excite only a limited number of these sublevels, sizable blockade effects are observed on an $\sim 0.1$ mm length scale extending blockade measurements into the near-macroscopic regime and enabling study of the dynamics of strongly coupled many-body high-$n$ Rydberg systems under carefully controlled conditions.

Figure 1

Schematic diagram of the apparatus. The inset shows the excitation scheme employed.

Figure 2

Calculated energy levels for Rydberg atom pairs with $\mathrm{\Lambda }=M_A+M_B=0$ near $n=50$. The internuclear separation $R$ is scaled by $n^{14/6}$ and the energy shift by $n^{-3}$ (see text). Axes expressed in practical units and scaled to $n=310$ are included for comparison to experiment. The states in red indicate those having the largest overlap with the unperturbed $50F-50F$ pair when expanded in the atomic basis.

Figure 3

Calculated relative excitation spectra for creation of two Rydberg atoms as a function of internuclear separation $R$. $R$ is scaled by $n^{14/6}$ and the detuning by $n^{-3}$. The laser linewidth is set to $0.002n^{-3}$ ($\sim 0.5$ MHz for $n=310$) and the spectra are normalized to 1 in the limit $R\to \infty$ with zero detuning. The atoms are assumed to be aligned (a) along the $z$ axis and (b) along the $x$ axis. The angular dependence is integrated in (c) (see text).

Figure 4

(a) Mean number, $\langle N_R\rangle$, of $n\sim 310$ Rydberg atoms excited by a 130-ns-long 461 nm laser pulse as a function of 893 nm IR laser power for the oven operating temperatures indicated. The inset shows the mean Rydberg atom number created per unit laser power $\mathcal{P},d\langle N_R\rangle /d\mathcal{P}(\mathcal{P}=0)$, for small laser powers as a function of beam density showing a linear increase with density. (b) Measured $Q$ values. The results in (a) and (b) are corrected for the detection efficiency $\eta$. (c) Calculated $Q$ values versus Rydberg excitation probability. The calculations assume the blockade probability $1-P_2$ is reduced by $20\%$ from the theoretical value (see text). $N$ specifies the assumed number of ground state atoms present in the excitation volume.

Figure 5

Measured $Q$ values expressed as a function of $\langle N_R\rangle$. The solid line shows the calculated values. The inset presents a typical Rydberg number distribution for $\langle N_R\rangle \sim 1$ (filled histogram: $P=0.9W,T=639{}^{\circ }\mathrm{C}$) together with a calculated distribution (open histogram: $N=329,P_R=0.005$, for the same $\langle N_R\rangle$). The line shows a Poissonian distribution for $\langle N_R\rangle =1$.